Josephson Current through a correlated quantum level: Andreev states and Pi-junction behavior

TL;DR

This paper investigates the Josephson effect in a quantum dot with a single level coupled to superconductors, exploring how Coulomb interactions influence Andreev states and Pi-junction behavior through various theoretical approaches.

Contribution

It compares multiple approximation methods to analyze the Josephson transport in a correlated quantum dot and clarifies conditions for Pi-junction behavior and Coulomb effects.

Findings

Coulomb interactions significantly affect Andreev states.

Conditions for observing Pi-junction behavior are identified.

Different approximation methods yield consistent insights.

Abstract

The Josephson transport and the electronic properties of a quantum dot characterized by a single level coupled to superconducting leads is analyzed. Different approximations are used and compared: the mean field approximation, the second order perturbation theory in the Coulomb interaction and the exact diagonalization in the zero band-width limit. The system exhibits a rich behavior as a function of the relevant parameters. We discuss in detail the conditions for the observation of Pi-junction behavior and the effect of Coulomb interactions on the Andreev states.